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2-1A Writing Equations Algebra 1 Glencoe McGraw-Hill Linda Stamper In Chapter 1 you translated phrases. Phrases are translated into mathematical expressions. Sentences are translated into equations or inequalities. Phrase The sum of 6 and a number 6 + n Sentence The sum of 6 and a number is fifteen. 6 + n = 15 Sentence Seven times a number is less than 50. 7n < 50 When choosing a variable for an unknown, it may be helpful to select a Sentences letter that must relates to the unknown value (for example: let have a represent a verb!age). When you translate from English to math, you must first determine whether the given problem is an expression (phrase) or a sentence. How do you know the difference? A sentence will have a verb. Some verbal expressions that suggest the equal sign are: is is as much as is the same as is identical to 3 times a number is 36. = 36 3n Identify the verb. Write the equal sign. Translate the expression to the left of the verb. Translate the expression to the right of the verb. The equal sign is like a brick wall – nothing crosses to the other side. Translate each sentence into an equation. 21 decreased by a number is 7. 21 n = 7 Twelve is the sum of nine and a number. 12 = 9 n 15 less than a number is 56. n 15 = 56 Five times the number a squared is three times the sum of b and c. 5a2 = 3 (b + c) The verb is where you write the equal sign. The equal sign is like a brick wall – nothing crosses to the other side. Example 1 Translate each sentence into an equation. a. Four times n is the difference of 30 and n. 4n = 30 - n b. Nine increased by a number is five squared. 9 + n = 52 c. Ten less than a number is fifty. n – 10 = 50 d. The sum of two and a number is 9. 2+n=9 e. A number decreased by five is four squared plus six. n - 5 = 42 + 6 f. The sum of a number and six, divided by three is eight. n6 8 3 Example 2 Translate each sentence into an equation. a. Fifteen more than z times 6 is y times 2 minus eleven. 6z + 15 = 2y - 11 b. Seven increased by a number is 21. 7 + n = 21 b c. A number b divided by three is six less than c. c 6 3 d. Twenty-seven times k is h squared decreased by 9. 27k = h2 - 9 e. Nine times a number subtracted from 95 equals 37. 95 – 9n = 37 f. Two plus the quotient of a number and 8 is 16. n 2 16 8 A formula is an algebraic equation that relates two or more quantities. Example 3 Translate each sentence into a formula. a. The perimeter of a rectangle equals two times the length = length plus two times the width. width P = 2l + 2w P = 2l + 2w length b. In a right triangle, the sum of the squares of the measures of the legs, a and b, is equal to the square of (hypotenuse) the hypotenuse c. (leg) c a2 + b2 = c2 a (leg) b c. The perimeter of a triangle is side a plus side b plus side c. P = a+ b + c width 2-A2 Pages 74-76 #13-18,23-26,35-36,50-51,57-68.